Question

Question 6(Multiple Choice Worth 1 points)
(08.05 MC)
The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x - 2). Find the vertex of g
(-1,-8)
(-3,-4)
(-1,-6)
(-5-6)​

Answer 1

Answer:

(-1,-6)

Step-by-step explanation:

We have the following function:

$f(x) = x^{2} + 6x + 3$

The following transformation is applied

$g(x) = f(x - 2)$

So

$g(x) = f(x - 2) = (x - 2)^{2} + 6(x - 2) + 3$

$g(x) = x^{2} - 4x + 4 + 6x - 12 + 3$

$g(x) = x^{2} + 2x - 5$

For a second order function in the format:

$g(x) = ax^{2} + bx + c$

The vertex is:

$V = (x_{v}, g(x_{v})$

In which

$x_{v} = -\frac{b}{2a}$

In this problem

$a = 1, b = 2$

So

$x_{v} = -\frac{2}{2*1} = -1$

Then

$g(x_{v}}) = g(-1) = (-1)^{2} +2(-1) - 5 =  -6$

So the correct answer is:

(-1,-6)